import Test.QuickCheck (Arbitrary(..), Gen)
import Cardinal
+import Comparisons (nearly_ge)
import FunctionValues
import Misc (factorial)
import Point
instance ThreeDimensional Tetrahedron where
center t = ((v0 t) + (v1 t) + (v2 t) + (v3 t)) `scale` (1/4)
contains_point t p =
- (b0 t p) >= 0 && (b1 t p) >= 0 && (b2 t p) >= 0 && (b3 t p) >= 0
+ (b0 t p) `nearly_ge` 0 &&
+ (b1 t p) `nearly_ge` 0 &&
+ (b2 t p) `nearly_ge` 0 &&
+ (b3 t p) `nearly_ge` 0
polynomial :: Tetrahedron -> (RealFunction Point)
y1, y2, y3, y4,
z1, z2, z3, z4 ]
where
- x1 = x_coord (v0 t)
- x2 = x_coord (v1 t)
- x3 = x_coord (v2 t)
- x4 = x_coord (v3 t)
- y1 = y_coord (v0 t)
- y2 = y_coord (v1 t)
- y3 = y_coord (v2 t)
- y4 = y_coord (v3 t)
- z1 = z_coord (v0 t)
- z2 = z_coord (v1 t)
- z3 = z_coord (v2 t)
- z4 = z_coord (v3 t)
+ (x1, y1, z1) = v0 t
+ (x2, y2, z2) = v1 t
+ (x3, y3, z3) = v2 t
+ (x4, y4, z4) = v3 t
-- | Computed using the formula from Lai & Schumaker, Definition 15.4,
-- page 436.